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Exam P Practice Problem 109 – counting insurance payments

Problem 109-A

Amounts of damages due to auto collision accidents follow a probability distribution whose density function is given by the following.

    \displaystyle  f(x) = \left\{ \begin{array}{ll}                   \displaystyle  \frac{3}{8000} \ (400-40x+x^2) &\ \ \ \ \ \ 0 < x < 20 \\           \text{ } & \text{ } \\          \displaystyle  0 &\ \ \ \ \ \ \text{otherwise} \\                              \end{array} \right.

When occurred, the collision damages are reimbursed by an insurance coverage subject to a deductible of 4.

Fifteen unrelated auto collision accidents have been reported. Determine the probability that exactly nine or ten of the accidents will be reimbursed by the insurance coverage.

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \bold 0 \bold . \bold 1 \bold 4 \bold 2

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 1 \bold 6 \bold 3

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 2 \bold 2 \bold 2

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 2 \bold 6 \bold 6

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 2 \bold 8 \bold 9

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Problem 109-B

Amounts of damages due to auto collision accidents follow a probability distribution whose density function is given by the following.

    \displaystyle  f(x) = \left\{ \begin{array}{ll}                   \displaystyle  \frac{3}{4000} \ (400-80x+4 x^2) &\ \ \ \ \ \ 0 < x < 10 \\           \text{ } & \text{ } \\          \displaystyle  0 &\ \ \ \ \ \ \text{otherwise} \\                              \end{array} \right.

When occurred, the damages are reimbursed by an insurance coverage subject to a deductible of 2.

Twelve unrelated auto collision accidents have been reported. Determine the probability that exactly six or seven of the accidents will not be reimbursed by the insurance coverage.

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \bold 0 \bold . \bold 1 \bold 8 \bold 4

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 2 \bold 2 \bold 5

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 4 \bold 0 \bold 8

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 4 \bold 2 \bold 7

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 4 \bold 5 \bold 0

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Answers

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